INST 251 (PID controllers and tuning), section 2

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Recommended schedule Day 1

Major topics: Introduction to differential calculus

Required reading: Lessons In Industrial Instrumentation “Introduction to calculus” and “The concept of differentiation” sections

Question 0: Research sources Discussion questions: 1 through 10

Lab Exercise: Pneumatic PID controller (question 62 + question 63) Day 2

Major topics: Differentiation of real signals Discussion questions: 11 through 20

Major topics: Proportional + Derivative control

Required reading: Lessons In Industrial Instrumentation “Derivative (rate) control” section Discussion questions: 21 through 30

Major topics: Proportional + Derivative control (continued) Discussion questions: 31 through 40

Lab Exercise: Lab questions (question 62)

Lab Exercise: Pneumatic PID controller due at the end of the day (question 62 + question 63)

Day 5

Feedback questions: 51 through 60 Labwork participation assessment: 61

Feedback questions due at the beginning of the day Lab Exercise: Mastery exam performance practice (question 64)

Exam 1: includes circuit-building performance exercise in Mastery portion Extra (not required)

Major topics: Introduction to differential calculus (continued) Discussion questions: 41 through 50

Practice problems 65 through end Impending deadlines

Working process due at the end of INST251 (in two more weeks)

Begin collecting mechanical parts for your process (pipe, tubing, pumps, fans, etc.).

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INSTRUCTOR CONTACT INFORMATION:

Tony Kuphaldt

(360)-752-8477 [office phone]

(360)-752-7277 [fax]

[email protected] DEPT/COURSE #: INST 251

CREDITS: 5 Lecture Hours: 26 Lab Hours: 66 Work-based Hours: 0 COURSE TITLE: PID Controllers and Tuning

COURSE OUTCOMES: Construct, configure, analyze, document, and efficiently diagnose instrumented systems using industry-standard PID controllers, as well as apply numerical calculus (differentiation and integration) to process data.

COURSE DESCRIPTION: This course teaches you how the most basic and widely-used control algorithm works: proportional-integral-derivative (PID). In this course you will see how the PID algorithm is implemented in pneumatic as well as electronic controllers, and also how to tune a PID controller for stability. Pre/Corequisite course: INST 250 (Final Control Elements)

COURSE OUTLINE: a course calendar in electronic format (Excel spreadsheet) resides on the Y:

network drive, and also in printed paper format in classroom DMC130, for convenient student access. This calendar is updated to reflect schedule changes resulting from employer recruiting visits, interviews, and other impromptu events. Course worksheets provide comprehensive lists of all course assignments and activities, with the first page outlining the schedule and sequencing of topics and assignment due dates.

These worksheets are available in PDF format at http://openbookproject.net/books/socratic/sinst

• INST251 Section 1 (Proportional control): 4 days theory and labwork

• INST251 Section 2 (Numerical Calculus): 4 days theory and labwork + 1 day for mastery/proportional Exams

• INST251 Section 3 (Integral Control): 4 days theory and labwork

• INST251 Section 4 (Derivative Control): 4 days theory and labwork + 1 day for mastery/proportional Exams

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STUDENT PERFORMANCE OBJECTIVES:

• Mastery exams (two per course): without references or notes, within a limited time (3 hours total for mastery and proportional exams), independently perform the following activities with no errors given a maximum of two attempts per exam sitting (up to three exam sittings allowed with a 10% score deduction levied on the proportional exam score if not passed on first sitting). At least 60% of exam questions are “Application” level or higher according to Bloom’s Taxonomy.

→ Exam 1: Build a circuit using an electromechanical relay to control two LEDs

→ Exam 1: Identify proper controller action (direct or reverse) for a given process

→ Exam 1: Determine the effect of a component change on the gain of a pneumatic controller mechanism

→ Exam 1: Calculate instrument calibration points given input and output ranges

→ Exam 1: Circuit Fault Review: determine possibility of open/short faults in a simple circuit given measured values (voltage, current)

→ Exam 1: INST241 Review: Identify proper wire and sheath colors for different thermocouple types

→ Exam 1: INST261 Review: Identify the purpose of overload heaters in motor control circuits

→ Exam 2: Build a circuit with a “smart” transmitter and use a HART communicator to re-range it

→ Exam 2: Determine the effect of a component fault or condition change in an automatically-controlled process

→ Exam 2: Perform either numerical differentiation or numerical integration on a simple mathematical function (graphed)

→ Exam 2: Calculate instrument calibration points given input and output ranges

→ Exam 2: Circuit Fault Review: determine possibility of open/short faults in a simple circuit given measured values (voltage, current)

→ Exam 2: INST241 Review: Identify suitability of basic flow-measuring instruments to different process fluids

→ Exam 2: INST262 Review: Define “class” and “division” ratings for classified industrial areas in the United States

• Proportional exams (two per course): without references or notes, independently solve several quantitative, conceptual, and diagnostic problems relating to the course subject. At least 60% of exam questions are “Application” level or higher according to Bloom’s Taxonomy.

• Lab exercises (two per course): in a team environment and with full access to references, notes, and instructor assistance; build and document functioning instrumentation systems as documented in the Lab Exercise questions found in all course worksheets. Each lab exercise includes a set of qualitative and conceptual questions to be answered individually without references or notes, and also lists mastery objectives for the lab exercise (must be completed with no errors) including:

→ Generate an accurate loop diagram compliant with ISA standards documenting your team’s system, personally verified by the instructor.

→ Calibrate all system instruments to specified accuracy using lab calibration equipment, personally verified by the instructor.

• Quizzes (daily): with access to notes, independently answer quantitative and conceptual questions relating to the day’s assigned questions and reading.

• Feedback question sets (four per course): ungraded exercises designed to review critical concepts and provide bidirectional student/instructor feedback on learning prior to exams.

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critical-thinking and life-long learning abilities, continually placing the student in an active rather than a passive role.

• Independent study: daily worksheet questions specify reading assignments, problems to solve, and experiments to perform in preparation (before) classroom theory sessions. Open-note quizzes and work inspections ensure accountability for this essential preparatory work. The purpose of this is to convey information and basic concepts, so valuable class time isn’t wasted transmitting bare facts, and also to foster the independent research ability necessary for self-directed learning in your career.

• Classroom sessions: a combination of Socratic discussion, short lectures, small-group problem-solving, and hands-on demonstrations/experiments review and illuminate concepts covered in the preparatory questions. The purpose of this is to develop problem-solving skills, strengthen conceptual understanding, and practice both quantitative and qualitative analysis techniques.

• Lab activities: an emphasis on constructing and documenting working projects (real instrumentation and control systems) to illuminate theoretical knowledge with practical contexts. Special projects off-campus or in different areas of campus (e.g. BTC’s Fish Hatchery) are encouraged. Hands-on troubleshooting exercises build diagnostic skills.

• Tours and guest speakers: quarterly tours of local industry and guest speakers on technical topics add breadth and additional context to the learning experience.

STUDENT ASSIGNMENTS/REQUIREMENTS: All assignments for this course are thoroughly documented in the following course worksheets located at:

http://openbookproject.net/books/socratic/sinst/index.html

• INST251 sec1.pdf

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EVALUATION AND GRADING STANDARDS: (out of 100% for the course grade)

• Mastery exams and mastery lab objectives = 50% of course grade

• Proportional exams = 40% (2 exams at 20% each)

• Lab questions = 10% (2 question sets at 5% each)

• Quiz penalty = -1% per failed quiz

• Tardiness penalty = -1% per incident (1 “free” tardy per course)

• Attendance penalty = -1% per hour (12 hours “sick time” per quarter)

• Repair bonus = +5% per repaired instrument (instrument’s broken and repaired statuses must be verified by the instructor)

All grades are criterion-referenced (i.e. no grading on a “curve”) 100% ≥ A ≥ 95% 95% > A- ≥ 90%

90% > B+ ≥ 86% 86% > B ≥ 83% 83% > B- ≥ 80%

80% > C+ ≥ 76% 76% > C ≥ 73% 73% > C- ≥ 70% (minimum passing course grade) 70% > D+ ≥ 66% 66% > D ≥ 63% 63% > D- ≥ 60% 60% > F

Failing a mastery exam will result in a 10% deduction from the proportional exam score, and you get a maximum of two re-takes (“sittings”) to pass new versions of the same mastery exam which must occur before the next exam date. Failure to pass the mastery within three sittings will result in a failing grade (F) for the course. Absence on a scheduled exam day will result in a 0% score for the proportional exam unless you provide documented evidence of an unavoidable emergency.

If any other “mastery” objectives are not completed by their specified deadlines, your overall grade for the course will be capped at 70% (C- grade), and you will have one more school day to complete the unfinished objectives. Failure to complete those mastery objectives by the end of that extra day (except in the case of documented, unavoidable emergencies) will result in a failing grade (F) for the course.

“Lab questions” are assessed by individual questioning, at any date after the respective lab objective (mastery) has been completed by your team. These questions serve to guide your completion of each lab exercise and confirm participation of each individual student. Grading is as follows: full credit for thorough, correct answers; half credit for partially correct answers; and zero credit for major conceptual errors. All lab questions must be answered by the due date of the lab exercise.

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• Course worksheets available for download in PDF format

• Lessons in Industrial Instrumentation textbook, available for download in PDF format

→ Access worksheets and book at: http://openbookproject.net/books/socratic/sinst

• Spiral-bound notebook for reading annotation, homework documentation, and note-taking.

• Instrumentation reference CD-ROM (free, from instructor). This disk contains many tutorials and datasheets in PDF format to supplement your textbook(s).

• Tool kit (see detailed list)

• Simple scientific calculator (non-programmable, non-graphing, no unit conversions, no numeration system conversions), TI-30Xa or TI-30XIIS recommended

ADDITIONAL INSTRUCTIONAL RESOURCES:

• The BTC Library hosts a substantial collection of textbooks and references on the subject of Instrumentation, as well as links in its online catalog to free Instrumentation e-book resources available on the Internet.

• “BTCInstrumentation” channel on YouTube (http://www.youtube.com/BTCInstrumentation), hosts a variety of short video tutorials and demonstrations on instrumentation.

• ISA Student Section at BTC meets regularly to set up industry tours, raise funds for scholarships, and serve as a general resource for Instrumentation students. Membership in the ISA is $10 per year, payable to the national ISA organization. Membership includes a complementary subscription to InTech magazine.

• ISA website (http://www.isa.org) provides all of its standards in electronic format, many of which are freely available to ISA members.

• Instrument Engineer’s Handbook, Volume 2: Process Control and Optimization, edited by B´ela Lipt´ak, published by CRC Press. 4th edition ISBN-10: 0849310814 ; ISBN-13: 978-0849310812.

• Purdy’s Instrument Handbook, by Ralph Dewey. ISBN-10: 1-880215-26-8. A pocket-sized field reference on basic measurement and control.

• Cad Standard (CadStd) or similar AutoCAD-like drafting software (useful for sketching loop and wiring diagrams). Cad Standard is a simplified clone of AutoCAD, and is freely available at:

http://www.cadstd.com

file INST251syllabus

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Sequence of second-year Instrumentation courses

INST 240 -- 6 cr

Pressure/Level Measurement

INST 241 -- 6 cr

Temp./Flow Measurement

INST 242 -- 5 cr

Analytical Measurement

INST 250 -- 5 cr

INST 251 -- 5 cr

PID Control Final Control Elements

Loop Tuning

INST 252 -- 4 cr

Data Acquisition Systems

INST 262 -- 5 cr

DCS and Fieldbus

INST 263 -- 5 cr

Control Strategies

Fall quarter Winter quarter Spring quarter Summer quarter

INST 230 -- 3 cr

Motor Controls

INST 231 -- 3 cr

PLC Programming

INST 232 -- 3 cr

PLC Systems

Offered 1^st week of

INST 200 -- 1 wk Intro. to Instrumentation

Job Prep I

Job Prep II INST 205 -- 1 cr

INST 206 -- 1 cr

INST25x, and INST26x courses Prerequisite for all INST24x,

Fall, Winter, and Spring quarters

Offered 1^st week of Fall, Winter, and Spring quarters

INST 260 -- 4 cr

ENGT 122 -- 6 cr

CAD 1: Basics including MATH 141 (Precalculus 1)

Core Electronics -- 3 qtrs

Prerequisite for INST206

(Only if 4th quarter was Summer: INST23x)

All courses completed? No

Yes Graduate!!!

INST 233 -- 3 cr

Protective Relays (elective)

CHEM&161 -- 5 cr

Chemistry

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first-year courses and enter the second year. Since students enter the second year of Instrumentation at four different times (beginnings of Summer, Fall, Winter, and Spring quarters), the particular course sequence for any student will likely be different from the course sequence of classmates.

Some second-year courses are only offered in particular quarters with those quarters not having to be in sequence, while others are offered three out of the four quarters and must be taken in sequence. The following layout shows four typical course sequences for second-year Instrumentation students, depending on when they first enter the second year of the program:

INST 240 -- 6 cr

INST 241 -- 6 cr

INST 242 -- 5 cr

Fall quarter INST 200 -- 1 wk

Intro. to Instrumentation

Winter quarter

Job Prep I INST 205 -- 1 cr

INST 250 -- 5 cr

Final Control Elements

INST 251 -- 5 cr

PID Control

Loop Tuning

INST 252 -- 4 cr

Spring quarter

INST 260 -- 4 cr

INST 262 -- 5 cr

DCS and Fieldbus

INST 263 -- 5 cr

Control Strategies

ENGT 122 -- 6 cr

CAD 1: Basics

Graduation!

Possible course schedules depending on date of entry into 2nd year

INST 240 -- 6 cr

INST 241 -- 6 cr

INST 242 -- 5 cr

Fall quarter INST 200 -- 1 wk

Winter quarter

INST 250 -- 5 cr

INST 251 -- 5 cr

PID Control

Loop Tuning

INST 252 -- 4 cr

Spring quarter

INST 260 -- 4 cr

INST 262 -- 5 cr

DCS and Fieldbus

INST 263 -- 5 cr

Control Strategies

ENGT 122 -- 6 cr

CAD 1: Basics

Graduation!

INST 240 -- 6 cr

INST 241 -- 6 cr

INST 242 -- 5 cr

Fall quarter Winter quarter

INST 250 -- 5 cr

INST 251 -- 5 cr

PID Control

Loop Tuning

INST 252 -- 4 cr

Spring quarter

INST 260 -- 4 cr

INST 262 -- 5 cr

DCS and Fieldbus

INST 263 -- 5 cr

Control Strategies

ENGT 122 -- 6 cr

CAD 1: Basics

Graduation!

INST 240 -- 6 cr

INST 241 -- 6 cr

INST 242 -- 5 cr

Fall quarter

Winter quarter

INST 250 -- 5 cr

INST 251 -- 5 cr

PID Control

Loop Tuning

INST 252 -- 4 cr Spring quarter

INST 260 -- 4 cr

INST 262 -- 5 cr

DCS and Fieldbus

INST 263 -- 5 cr

Control Strategies

ENGT 122 -- 6 cr

CAD 1: Basics

Graduation!

INST 200 -- 1 wk

Job Prep II INST 206 -- 1 cr Sept.

Dec.

Jan.

Mar.

April

June

Sept.

Dec.

Jan.

Mar.

April

June

Jan.

Mar.

April

June

Sept.

Dec.

April

June

Sept.

Dec.

Jan.

Mar.

Beginning in Summer Beginning in Fall Beginning in Winter Beginning in Spring

CHEM&161 -- 5 cr

Chemistry

CHEM&161 -- 5 cr

Chemistry

CHEM&161 -- 5 cr

Chemistry

CHEM&161 -- 5 cr

Chemistry

Summer quarter INST 230 -- 3 cr

Motor Controls

INST 231 -- 3 cr

PLC Programming

INST 232 -- 3 cr

PLC Systems

July

Aug.

INST 233 -- 3 cr

Motor Controls

INST 231 -- 3 cr

PLC Programming

INST 232 -- 3 cr

PLC Systems

July

INST 233 -- 3 cr

Motor Controls

INST 231 -- 3 cr

PLC Programming

INST 232 -- 3 cr

PLC Systems

July

INST 233 -- 3 cr

Motor Controls

INST 231 -- 3 cr

PLC Programming

INST 232 -- 3 cr

PLC Systems

July

INST 233 -- 3 cr

Aug.

file sequence

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General Student Expectations

Your future employer expects you to: show up for work on time, prepared, every day; to work safely, efficiently, conscientiously, and with a clear mind; to be self-directed and take initiative; to follow through on all commitments; and to take responsibility for all your actions and for the consequences of those actions.

Instrument technicians work on highly complex, mission-critical measurement and control systems, where incompetence and/or lack of integrity invites disaster. This is also why employers check legal records and social networking websites for signs of irresponsibility when considering a graduate for hire. Substance abuse is particularly noteworthy since it impairs reasoning, and this is first and foremost a “thinking” career.

Mastery: You are expected to master the fundamentals of your chosen craft. “Mastery” assessments challenge you to demonstrate 100% competence in specific knowledge and skill areas (with multiple opportunities to re-try if necessary). Failure to fulfill any mastery objective(s) by the deadline results in your grade for that course being capped at a C-, with one more day given to demonstrate mastery. Failure to fulfill any mastery objective(s) by the end of that extra day will result in a failing grade for the course.

Punctuality and Attendance: You are expected to arrive on time, every scheduled day, and attend for the full duration of the scheduled day, just as you would for a job. If a session begins at 12:00 noon, 12:00:01 is considered late. Each student has 12 hours of “sick time” per quarter applicable to absences not verifiably employment-related, school-related, weather-related, or required by law. Each student must confer with the instructor to apply these hours to any missed time – this is not done automatically for the student. Students may donate unused “sick time” to whomever they specifically choose. You must contact your instructor and team members immediately if you know you will be late or absent, and it is your responsibility to catch up on all missed activities. Absence on an exam day will result in a zero score for that exam, unless due to a documented emergency.

Time Management: You are expected to budget and use your time productively, just as you are expected to budget and use time productively on the job. It is important for your learning that you remain “on task”

during the entire school day and reserve enough time outside of school to complete all of your homework.

Frivolous use of computers and smart phones (e.g. games, social networking, internet surfing) is unacceptable when there is work to be done. Trips to the cafeteria for food or coffee, as well as breaks for smoking, should similarly take place on your own time. These expectations are commonplace in industrial work environments.

Most students find their homework requires a minimum of 3 hours of study time per day. Question 0 (included in every worksheet) lists practical tips for creating more study time.

Independent Study: Industry advisors and successful graduates consistently identify self-directed learning as a vital skill for this career, more important even than trade-specific knowledge and skills. All second-year Instrumentation courses follow an “inverted” model where lecture is replaced by independent study outside of class, and class time is spent answering questions and demonstrating learning. Showing up to class unprepared (e.g. incomplete homework assignments) is unprofessional and impedes your learning. Question 0, which is included in every worksheet, lists practical study tips.

Problem-solving: Industry advisors and successful graduates also consistently identify general problem- solving as a vital skill for this career, more important even than trade-specific knowledge and skills. You are expected to take every reasonable measure to solve problems on your own before asking for assistance from anyone else. If you are confused on of the homework problems, that is okay, but you are expected to apply problem-solving strategies modeled by your instructor and to precisely identify where you are confused so your instructor will be able to give you targeted help. Asking classmates to solve the problem for you is unacceptable because it circumvents your responsibility to solve the problem yourself. When troubleshooting systems in lab you are expected to use appropriate tools to perform diagnostic tests (e.g. don’t just visually inspect for faults), as well as consult the equipment manual(s) before seeking help. If you identify failed

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Safety: You are expected to work safely in the lab just as you will be on the job. This includes wearing proper attire (safety glasses and closed-toed shoes in the lab at all times), implementing lock-out/tag-out procedures when working on circuits over 24 volts, using ladders to reach high places rather than standing on tables or chairs, and correctly using all tools.

Cleanliness: You are expected to keep your work area clean and orderly just as you will be on the job. This includes discarding all food and drink containers every day, putting tools and parts back where they belong after you are finished with them, and participating in all scheduled lab clean-up sessions.

Teamwork: You will work in instructor-assigned teams to complete lab assignments, just as you will work in teams to complete complex assignments on the job. As part of a team, you must keep your teammates informed of your whereabouts in the event you must step away from the lab or cannot attend for any reason.

Any student regularly compromising team performance through lack of participation, absence, tardiness, disrespect, unsafe work, or other disruptive behavior(s) will be given the choice of either completing all labwork independently for the remainder of the quarter or receiving a failing grade for the course.

Cooperation: The structure of these courses naturally lends itself to cooperation between students. Working together, students have a large impact on each others’ learning. You are expected to take this role seriously, offering real help when needed and not absolving classmates of their responsibility to do the hard work themselves. Solving problems for classmates and/or doing assigned work for classmates is unacceptable because these actions circumvent learning. The best form of help you can give to your struggling classmates is to share with them your tips on independent learning and general problem-solving. A practical way to offer guidance is to ask questions leading to the solution rather than merely providing the solution.

Academic Engagement: Instrumentation is a complex career, full of challenges requiring creative and critical thinking. As industry advisors have said, “Being an instrument technician is as close as you get to doing engineering without a four-year (Bachelor’s) degree.” The only way to prepare for the challenges of being an instrument technician is to exercise that same level of creative and critical thinking before you step into the career, mastering first principles of science and general problem-solving strategies rather than focusing on low-level cognitive exercises such as memorization and procedural solutions. This also means personally involving yourself in every learning exercise, not being content to merely observe others.

Individual (unassisted) performance is the gold standard for learning: unless and until you can consistently perform on your own, you haven’t learned!

Grades: Grades are to learning as a fuel gauge in a vehicle is to the actual amount of fuel stored in the tank.

Like a fuel gauge, a grade is an imperfect representation of reality, and as such may be skewed upward or downward by factors unrelated to the reality it’s supposed to measure. Far too many students worry about the gauge’s reading when they should be worried about how much fuel is in the tank! As an Instrumentation student you will be expected to prioritize learning over grades, because only learning will help you on the job. This, for example, is why extra-credit assignments are customized to each student’s needs based on their weakest areas rather than arbitrarily assigned to pad a student’s grade.

Representation: You are an ambassador for this program. Your actions, whether on tours, during a jobshadow or internship, or while employed, can open or shut doors of opportunity for other students. Most of the opportunities open to you as a BTC graduate were earned by the good work of previous graduates, and as such you owe them a debt of gratitude. Future graduates depend on you to do the same.

Responsibility For Actions: If you lose or damage college property (e.g. lab equipment), you must find, repair, or help replace it. If your represent BTC poorly to employers (e.g. during a tour or an internship), you must make amends. The general rule here is this: “If you break it, you fix it!”

file expectations

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General grading and evaluation standards Assessment criteria

• Mastery (all must be mastered – constitutes first 50% of course grade)

• Mastery section of each lab exercise (unlimited attempts)

• Mastery section of each exam including the hands-on circuit building or troubleshooting activity (up to two attempts per sitting; up to three sittings); or mastery capstone assessment (unlimited attempts)

• Proportional (grades based on quality of fulfillment, counts toward last 50% of course grade)

• Labwork, consisting of questions answered in an oral and demonstrative format (10% of grade)

• Proportional section of all exams (20% of grade)

• Feedback questions for all sections (20% of grade)

• Daily quizzes demonstrating preparation for theory sessions (-1% per failed quiz)

• Daily punctuality (-1% per incident of tardiness)

• Attendance (-1% per hour past allotted “sick time”)

• Repaired instruments (+5% per item) – Instrument identified in need of repair by the instructor Negative weighting represent objectives where 100% passing is a basic expectation (passing every quiz, punctuality every day, no accidents, etc.). Perfectly meeting these expectations does not count toward your grade, but failing to meet these basic expectations will result in grade loss.

Grading scale

All grades are criterion-referenced (i.e. no grading on a “curve”)

• 100% ≥ A ≥ 95% 95% > A- ≥ 90%

• 90% > B+ ≥ 86% 86% > B ≥ 83% 83% > B- ≥ 80%

• 80% > C+ ≥ 76% 76% > C ≥ 73% 73% > C- ≥ 70% (minimum passing course grade)

• 70% > D+ ≥ 66% 66% > D ≥ 63% 63% > D- ≥ 60% 60% > F

The proportional section of an exam may be taken only after taking the mastery section. Failing the mastery exam will result in a 50% deduction from the proportional exam score, and you get a maximum of two re-takes to pass the mastery which must occur within three school days of the first attempt. Failure to pass the mastery within three sittings will result in a failing grade for the course. Absence on a scheduled exam day will result in a 0% score for the proportional exam unless you provide documented evidence of an unavoidable emergency. You may receive half-credit on missed proportional exam questions after grading by explaining your original mistake(s) and providing completely corrected responses on the first attempt.

If any other “mastery” objectives are not completed by their specified deadlines, your overall grade for the course will be capped at 70% (C- grade), and you will have one more course day to complete the unfinished objectives. Failure to complete those mastery objectives by the end of that extra day (except in the case of documented, unavoidable emergencies) will result in a failing grade (F) for the course.

Answers to “feedback questions” are due at the end of each course section. Full credit is given for each question correctly and thoroughly answered, half credit for each question either not fully answered or containing minor errors, and zero credit for major conceptual errors. Late submissions will receive zero credit, unless due to a documented emergency.

“Lab questions” are assessed in a group format where students take turns answering questions from the list at the instructor’s prompting. Grading follows the same rubric as for feedback questions: full credit for thorough, correct answers; half credit for partially correct answers, and zero credit for major conceptual errors. If you are absent during this assessment, you must submit written answers to all of the lab questions, which will be graded by the instructor.

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Wrenches

• Combination (box- and open-end) wrench set, 1/4” to 3/4” – the most important wrench sizes are 7/16”, 1/2”, 9/16”, and 5/8”; get these immediately!

• Adjustable wrench, 6” handle (sometimes called “Crescent” wrench)

• Hex wrench (“Allen” wrench) set, fractional – 1/16” to 3/8”

• Optional: Hex wrench (“Allen” wrench) set, metric – 1.5 mm to 10 mm

• Optional: Miniature combination wrench set, 3/32” to 1/4” (sometimes called an “ignition wrench” set) Note: when turning a bolt, nut, or tube fitting with a hexagonal body, the preferred ranking of hand tools to use (from first to last) is box-end wrench or socket, open-end wrench, and finally adjustable wrench.

Pliers should never be used to turn the head of a fitting or fastener unless it is absolutely unavoidable!

Pliers

• Needle-nose pliers

• Tongue-and-groove pliers (sometimes called “Channel-lock” pliers)

• Diagonal wire cutters (sometimes called “dikes”) Screwdrivers

• Slotted, 1/8” and 1/4” shaft

• Phillips, #1 and #2

• Jeweler’s screwdriver set

• Optional: Magnetic multi-bit screwdriver (e.g. Klein Tools model 70035)

Note: when driving a screw, one should choose a screwdriver engaging the maximum amount of surface area on the screw’s head in order to reduce stress on the screw.

Measurement tools

• Tape measure. 12 feet minimum

• Optional: Vernier calipers, bubble level Electrical

• Multimeter, Fluke model 87-IV or better

• Wire strippers/terminal crimpers with a range including 10 AWG to 18 AWG wire

• Soldering iron (10 to 40 watt) and rosin-core solder

• Package of compression-style fork terminals (e.g. 14 to 18 AWG wire size, #10 stud size)

• Optional: Test leads with banana-style plugs Safety

• Safety glasses or goggles (available at BTC bookstore)

• Earplugs (available at BTC bookstore) Miscellaneous

• Simple scientific calculator (non-programmable, non-graphing, no conversions), TI-30Xa or TI-30XIIS recommended. Required for some exams!

• Teflon pipe tape

• Utility knife

• Optional: Flashlight

An inexpensive source of high-quality tools is your local pawn shop. Look for name-brand tools with unlimited lifetime guarantees (e.g. Sears “Craftsman” brand, Snap-On, etc.). Some local tool suppliers give BTC student discounts as well!

file tools

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Methods of instruction

This course develops self-instructional and diagnostic skills by placing students in situations where they are required to research and think independently. In all portions of the curriculum, the goal is to avoid a passive learning environment, favoring instead active engagement of the learner through reading, reflection, problem-solving, and experimental activities. The curriculum may be roughly divided into two portions:

theory and practical.

Theory

In the theory portion of each course, students independently research subjects prior to entering the classroom for discussion. This means working through all the day’s assigned questions as completely as possible. This usually requires a fair amount of technical reading, and may also require setting up and running simple experiments. At the start of the classroom session, the instructor will check each student’s preparation with a quiz. Students then spend the rest of the classroom time working in groups and directly with the instructor to thoroughly answer all questions assigned for that day, articulate problem-solving strategies, and to approach the questions from multiple perspectives. To put it simply: fact-gathering happens outside of class and is the individual responsibility of each student, so that class time may be devoted to the more complex tasks of critical thinking and problem solving where the instructor’s attention is best applied.

Classroom theory sessions usually begin with either a brief Q&A discussion or with a “Virtual Troubleshooting” session where the instructor shows one of the day’s diagnostic question diagrams while students propose diagnostic tests and the instructor tells those students what the test results would be given some imagined (“virtual”) fault scenario, writing the test results on the board where all can see. The students then attempt to identify the nature and location of the fault, based on the test results.

Each student is free to leave the classroom when they have completely worked through all problems and have answered a “summary” quiz designed to gauge their learning during the theory session. If a student finishes ahead of time, they are free to leave, or may help tutor classmates who need extra help.

The express goal of this “inverted classroom” teaching methodology is to help each student cultivate critical-thinking and problem-solving skills, and to sharpen their abilities as independent learners. While this approach may be very new to you, it is more realistic and beneficial to the type of work done in instrumentation, where critical thinking, problem-solving, and independent learning are “must-have” skills.

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In the lab portion of each course, students work in teams to install, configure, document, calibrate, and troubleshoot working instrument loop systems. Each lab exercise focuses on a different type of instrument, with a eight-day period typically allotted for completion. An ordinary lab session might look like this:

(1) Start of practical (lab) session: announcements and planning (a) The instructor makes general announcements to all students

(b) The instructor works with team to plan that day’s goals, making sure each team member has a clear idea of what they should accomplish

(2) Teams work on lab unit completion according to recommended schedule:

(First day) Select and bench-test instrument(s) (One day) Connect instrument(s) into a complete loop

(One day) Each team member drafts their own loop documentation, inspection done as a team (with instructor)

(One or two days) Each team member calibrates/configures the instrument(s) (Remaining days, up to last) Each team member troubleshoots the instrument loop

(3) End of practical (lab) session: debriefing where each team reports on their work to the whole class Troubleshooting assessments must meet the following guidelines:

• Troubleshooting must be performed on a system the student did not build themselves. This forces students to rely on another team’s documentation rather than their own memory of how the system was built.

• Each student must individually demonstrate proper troubleshooting technique.

• Simply finding the fault is not good enough. Each student must consistently demonstrate sound reasoning while troubleshooting.

• If a student fails to properly diagnose the system fault, they must attempt (as many times as necessary) with different scenarios until they do, reviewing any mistakes with the instructor after each failed attempt.

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Distance delivery methods

Sometimes the demands of life prevent students from attending college 6 hours per day. In such cases, there exist alternatives to the normal 8:00 AM to 3:00 PM class/lab schedule, allowing students to complete coursework in non-traditional ways, at a “distance” from the college campus proper.

For such “distance” students, the same worksheets, lab activities, exams, and academic standards still apply. Instead of working in small groups and in teams to complete theory and lab sections, though, students participating in an alternative fashion must do all the work themselves. Participation via teleconferencing, video- or audio-recorded small-group sessions, and such is encouraged and supported.

There is no recording of hours attended or tardiness for students participating in this manner. The pace of the course is likewise determined by the “distance” student. Experience has shown that it is a benefit for

“distance” students to maintain the same pace as their on-campus classmates whenever possible.

In lieu of small-group activities and class discussions, comprehension of the theory portion of each course will be ensured by completing and submitting detailed answers for all worksheet questions, not just passing daily quizzes as is the standard for conventional students. The instructor will discuss any incomplete and/or incorrect worksheet answers with the student, and ask that those questions be re-answered by the student to correct any misunderstandings before moving on.

Labwork is perhaps the most difficult portion of the curriculum for a “distance” student to complete, since the equipment used in Instrumentation is typically too large and expensive to leave the school lab facility. “Distance” students must find a way to complete the required lab activities, either by arranging time in the school lab facility and/or completing activities on equivalent equipment outside of school (e.g.

at their place of employment, if applicable). Labwork completed outside of school must be validated by a supervisor and/or documented via photograph or videorecording.

Conventional students may opt to switch to “distance” mode at any time. This has proven to be a benefit to students whose lives are disrupted by catastrophic events. Likewise, “distance” students may switch back to conventional mode if and when their schedules permit. Although the existence of alternative modes of student participation is a great benefit for students with challenging schedules, it requires a greater investment of time and a greater level of self-discipline than the traditional mode where the student attends school for 6 hours every day. No student should consider the “distance” mode of learning a way to have more free time to themselves, because they will actually spend more time engaged in the coursework than if they attend school on a regular schedule. It exists merely for the sake of those who cannot attend during regular school hours, as an alternative to course withdrawal.

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Focus on principles, not procedures

• Effective problem-solvers don’t bother trying to memorize procedures for problem-solving because procedures are too specific to the type of problem. Rather, they internalize general principles applicable to a wide variety of problems.

• When asking questions about some new subject, concentrate on “why” rather than “how” or “what.”

Cultivate meta-cognitive skills (the ability to monitor your own thinking on a subject)!

• Whenever you get “stuck” trying to understand a concept, clearly identify where you are getting stuck, and where things stop making sense.

• When you think you understand a concept, test your understanding by explaining it in your own words.

You can do this by trying to explain it to a willing classmate, or by imagining yourself trying to explain it to someone. If you cannot clearly explain a concept to someone else, you do not understand it well enough yourself !

• The technique of trying to explain a concept also works well to identify where you are stuck. The point at which you find yourself unable to clearly articulate the concept is very likely the exact point of your misconception or confusion.

Join or create a study group with like-minded classmates!

• Read the textbook assignments together.

• Solve assigned problems together.

• Collectively identify difficult concepts and areas needing clarification, to bring up later during class.

• Take turns trying to explain complicated concepts to each other, then critiquing those explanations.

Eliminate distractions in your life!

• Time-wasting technologies: televisions, internet, video games, mobile phones, etc.

• Unhelpful friends, unhealthy relationships, etc.

Make use of “wasted” time to study!

• Carefully plan your lab sessions with your teammates to reserve a portion of each day’s lab time for study.

• Bring a meal to school every day and use your one-hour lunch break for study instead of eating out.

This will not just save you time, but also money!

• Plan to arrive at school at least a half-hour early (the doors unlock at 7:00 AM) and use the time to study as opposed to studying late at night. This also helps guard against tardiness in the event of unexpected delays, and ensures you a better parking space!

Take responsibility for your learning and your life!

• Do not procrastinate, waiting until the last minute to do something.

• Obtain all the required books, and any supplementary study materials available to you. If the books cost too much, look on the internet for used texts (www.amazon.com, www.half.com, etc.) and use the money from the sale of your television and video games to buy them!

• Make an honest attempt to solve problems before asking someone else to help you. Being able to problem-solve is a skill that will improve only if you continue to work at it.

• If you detect trouble understanding a basic concept, address it immediately. Never ignore an area of confusion, believing you will pick up on it later. Later may be too late!

• Do not wait for others to do things for you. No one is going to make extra effort purely on your behalf.

. . . And the number one tip for success . . .

• Realize that there are no shortcuts to learning. Every time you seek a shortcut, you are actually cheating yourself out of a learning opportunity!!

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Creative Commons License

This worksheet is licensed under the Creative Commons Attribution License, version 1.0. To view a copy of this license, visit http://creativecommons.org/licenses/by/1.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA. The terms and conditions of this license allow for free copying, distribution, and/or modification of all licensed works by the general public.

Simple explanation of Attribution License:

The licensor (Tony Kuphaldt) permits others to copy, distribute, display, and otherwise use this work. In return, licensees must give the original author(s) credit. For the full license text, please visit http://creativecommons.org/licenses/by/1.0/on the internet.

More detailed explanation of Attribution License:

Under the terms and conditions of the Creative Commons Attribution License, you may make freely use, make copies, and even modify these worksheets (and the individual “source” files comprising them) without having to ask me (the author and licensor) for permission. The one thing you must do is properly credit my original authorship. Basically, this protects my efforts against plagiarism without hindering the end-user as would normally be the case under full copyright protection. This gives educators a great deal of freedom in how they might adapt my learning materials to their unique needs, removing all financial and legal barriers which would normally hinder if not prevent creative use.

Nothing in the License prohibits the sale of original or adapted materials by others. You are free to copy what I have created, modify them if you please (or not), and then sell them at any price. Once again, the only catch is that you must give proper credit to myself as the original author and licensor. Given that these worksheets will be continually made available on the internet for free download, though, few people will pay for what you are selling unless you have somehow added value.

Nothing in the License prohibits the application of a more restrictive license (or no license at all) to derivative works. This means you can add your own content to that which I have made, and then exercise full copyright restriction over the new (derivative) work, choosing not to release your additions under the same free and open terms. An example of where you might wish to do this is if you are a teacher who desires to add a detailed “answer key” for your own benefit but not to make this answer key available to anyone else (e.g. students).

Note: the text on this page is not a license. It is simply a handy reference for understanding the Legal Code (the full license) - it is a human-readable expression of some of its key terms. Think of it as the user-friendly interface to the Legal Code beneath. This simple explanation itself has no legal value, and its contents do not appear in the actual license.

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• Metric prefixes

• Yotta = 10²⁴ Symbol: Y

• Zeta = 10²¹ Symbol: Z

• Exa = 10¹⁸ Symbol: E

• Peta = 10¹⁵ Symbol: P

• Tera = 10¹² Symbol: T

• Giga = 10⁹ Symbol: G

• Mega = 10⁶Symbol: M

• Kilo = 10³ Symbol: k

• Hecto = 10² Symbol: h

• Deca = 10¹Symbol: da

• Deci = 10⁻¹ Symbol: d

• Centi = 10⁻² Symbol: c

• Milli = 10⁻³ Symbol: m

• Micro = 10⁻⁶ Symbol: µ

• Nano = 10⁻⁹ Symbol: n

• Pico = 10⁻¹² Symbol: p

• Femto = 10⁻¹⁵ Symbol: f

• Atto = 10⁻¹⁸ Symbol: a

• Zepto = 10⁻²¹ Symbol: z

• Yocto = 10⁻²⁴ Symbol: y

10⁰ 10³ 10⁶ 10⁹

10¹² 10^-3 10^-6 10^-9 10^-12

(none) kilo

mega giga

tera milli micro nano pico

k M G

T m µ n p

10^-2 10^-1 10¹ 10²

deci centi deca

hecto

h da d c

METRIC PREFIX SCALE

• Conversion formulae for temperature

• ^oF = (^oC)(9/5) + 32

• ^oC = (^oF - 32)(5/9)

• ^oR =^oF + 459.67

• K =^oC + 273.15

Conversion equivalencies for distance 1 inch (in) = 2.540000 centimeter (cm) 1 foot (ft) = 12 inches (in)

1 yard (yd) = 3 feet (ft) 1 mile (mi) = 5280 feet (ft)

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Conversion equivalencies for volume

1 gallon (gal) = 231.0 cubic inches (in³) = 4 quarts (qt) = 8 pints (pt) = 128 fluid ounces (fl. oz.)

= 3.7854 liters (l)

1 milliliter (ml) = 1 cubic centimeter (cm³)

Conversion equivalencies for velocity

1 mile per hour (mi/h) = 88 feet per minute (ft/m) = 1.46667 feet per second (ft/s) = 1.60934 kilometer per hour (km/h) = 0.44704 meter per second (m/s) = 0.868976 knot (knot – international)

Conversion equivalencies for mass

1 pound (lbm) = 0.45359 kilogram (kg) = 0.031081 slugs

Conversion equivalencies for force 1 pound-force (lbf) = 4.44822 newton (N)

Conversion equivalencies for area

1 acre = 43560 square feet (ft²) = 4840 square yards (yd²) = 4046.86 square meters (m²)

Conversion equivalencies for common pressure units (either all gauge or all absolute) 1 pound per square inch (PSI) = 2.03602 inches of mercury (in. Hg) = 27.6799 inches of water (in.

W.C.) = 6.894757 kilo-pascals (kPa) = 0.06894757 bar

1 bar = 100 kilo-pascals (kPa) = 14.504 pounds per square inch (PSI)

Conversion equivalencies for absolute pressure units (only)

1 atmosphere (Atm) = 14.7 pounds per square inch absolute (PSIA) = 101.325 kilo-pascals absolute (kPaA) = 1.01325 bar (bar) = 760 millimeters of mercury absolute (mmHgA) = 760 torr (torr)

Conversion equivalencies for energy or work

1 british thermal unit (Btu – “International Table”) = 251.996 calories (cal – “International Table”)

= 1055.06 joules (J) = 1055.06 watt-seconds (W-s) = 0.293071 watt-hour (W-hr) = 1.05506 x 10¹⁰ ergs (erg) = 778.169 foot-pound-force (ft-lbf)

Conversion equivalencies for power

1 horsepower (hp – 550 ft-lbf/s) = 745.7 watts (W) = 2544.43 british thermal units per hour (Btu/hr) = 0.0760181 boiler horsepower (hp – boiler)

Acceleration of gravity (free fall), Earth standard

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Speed of light in a vacuum (c) = 2.9979 × 10⁸meters per second (m/s) = 186,281 miles per second (mi/s)

Avogadro’s number (NA) = 6.022 × 10²³per mole (mol⁻¹) Electronic charge (e) = 1.602 × 10⁻¹⁹ Coulomb (C)

Boltzmann’s constant (k) = 1.38 × 10⁻²³ Joules per Kelvin (J/K)

Stefan-Boltzmann constant (σ) = 5.67 × 10⁻⁸ Watts per square meter-Kelvin⁴ (W/m²·K⁴) Molar gas constant (R) = 8.314 Joules per mole-Kelvin (J/mol-K)

Properties of Water

Freezing point at sea level = 32ôF = 0ôC Boiling point at sea level = 212ôF = 100ôC

Density of water at 4ôC = 1000 kg/m³= 1 g/cm³ = 1 kg/liter = 62.428 lb/ft³ = 1.94 slugs/ft³ Specific heat of water at 14ôC = 1.00002 calories/g·ôC = 1 BTU/lb·ôF = 4.1869 Joules/g·ôC Specific heat of ice ≈ 0.5 calories/g·ôC

Specific heat of steam ≈ 0.48 calories/g·^oC

Absolute viscosity of water at 20^oC = 1.0019 centipoise (cp) = 0.0010019 Pascal-seconds (Pa·s) Surface tension of water (in contact with air) at 18^oC = 73.05 dynes/cm

pH of pure water at 25^oC = 7.0 (pH scale = 0 to 14)

Properties of Dry Air at sea level

Density of dry air at 20^oC and 760 torr = 1.204 mg/cm³ = 1.204 kg/m³ = 0.075 lb/ft³ = 0.00235 slugs/ft³

Absolute viscosity of dry air at 20^oC and 760 torr = 0.018 centipoise (cp) = 1.8 × 10⁻⁵ Pascal- seconds (Pa·s)

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Question 0

How to get the most out of academic reading:

• Articulate your thoughts as you read (i.e. “have a conversation” with the author). This will develop metacognition: active supervision of your own thoughts. Write your thoughts as you read, noting points of agreement, disagreement, confusion, epiphanies, and connections between different concepts or applications. These notes should also document important math formulae, explaining in your own words what each formula means and the proper units of measurement used.

• Outline, don’t highlight! Writing your own summary or outline is a far more effective way to comprehend a text than simply underlining and highlighting key words. A suggested ratio is writing one sentence of your own thoughts per paragraph of text read. Include in your outline any points where you either disagree or are confused, so that you may review these points in the future.

• Work through all mathematical exercises shown within the text, to ensure you understand all the steps.

• Imagine explaining concepts you’ve just learned to someone else. Teaching forces you to distill concepts to their essence, thereby clarifying those concepts, revealing assumptions, and exposing misconceptions.

Your goal is to create the simplest explanation that is still technically accurate.

How to effectively problem-solve and troubleshoot:

• Study principles, not procedures. Don’t be satisfied with merely knowing the steps necessary to compute solutions – challenge yourself to learn why those solutions work. If you can’t explain “why,” you really haven’t learned the most important part.

• Sketch a diagram to help visualize the problem. When building a real system, always prototype it on paper and analyze its function before constructing it.

• Identify what it is you need to solve, identify all relevant data, identify all units of measurement, identify any general principles or formulae linking the given information to the solution, and then identify any

“missing pieces” to a solution. Annotate all diagrams with this data.

• Perform “thought experiments” to explore the effects of different conditions for theoretical problems.

When troubleshooting real systems, perform diagnostic tests rather than visually inspecting for faults.

• Simplify the problem and solve that simplified problem to identify strategies applicable to the original problem (e.g. change quantitative to qualitative, or visa-versa; substitute easier numerical values;

eliminate confusing details; add details to eliminate unknowns; consider simple limiting cases; apply an analogy). Often you can add or remove components in a malfunctioning system to simplify it as well and better identify the nature and location of the problem.

• Work “backward” from a hypothetical solution to a new set of given conditions.

How to create more time for study:

• Kill your television and video games. Seriously – these are incredible wastes of time. Eliminate distractions (e.g. cell phone, internet access, conversations) in your place and time of study.

• Use your “in between” time productively. Don’t waste time driving off campus to eat lunch. Arrive to school early. If you finish your assigned work early, begin studying the next day’s material.

Above all, cultivate persistence in your studies. Persistent effort is necessary to master anything non-trivial. The keys to persistence are (1) having the desire to achieve that mastery, and (2) realizing

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Question 1

Write an equation to solve for the downstream pressure at this control valve, given the upstream pressure (P1), Cv factor, specific gravity (Gf) of the process liquid, and flow rate (Q):

P₁ C_v P₂

Q

P2 (formula) =

Then, solve for P2 (in units of PSI) supposing the following conditions:

• Q = 130 GPM

• Gf = 0.83

• P¹ = 260 kPa

• Cv = 35

P2 = PSI

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Question 2

A bored child is traveling in a car with his parents, and decides to pass the time by writing mileage values displayed by the odometer at different times, and then noting those times next to the distances:

Odometer reading Time (miles) (hour:minute)

60,344.1 2:14

60,346.3 2:17

60,347.1 2:18

60,351.7 2:25

60,353.9 2:27

60,357.4 2:30

60,359.5 2:35

Calculate the average speed of the car between the following times:

• Between 2:17 and 2:18, average speed = MPH

Then, compare the average speeds taken in the first three intervals with the average speed over the sum of those intervals (2:17 to 2:27). What does this tell us about the calculation of speed based on distance and time measurements?

Suggestions for Socratic discussion

• In parts of the country with toll booths, you can get a speeding ticket automatically issued to you based on the time it took you to drive from one toll station to another. Explain how this works, and if there is any way to “beat the system” (i.e. speed without getting a time-based speeding ticket).

• Identify the arithmetic operations needed to compute rates of change, such as speed.

• This sort of repetitive calculation lends itself well to a programmable calculator, or to a spreadsheet program running on a personal computer. If you have some familiarity with spreadsheets, try building one to calculate average speeds given this table of distance values!

file i01502 Question 3

In areas of the United States where toll booths are used to monitor passenger vehicle travel, you can get a speeding ticket if your travel time between two toll booths is too short. Explain how this method of ticketing speeders is valid even if the exact speed of the vehicle at any specific time is unknown between toll booths. Also, explain how it is possible to exceed the speed limit between toll booths without getting ticketed based on elapsed time between tolls.

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A bored operator is filling a large tank with water from different sources, the flow rates from those sources being variable over time. He decides to pass the time by writing water volume values displayed by the level indicator (calibrated in gallons) at different times, and then noting those times next to the volumes:

Level indicator Time (gallons) (hour:minute)

120.7 9:17

1005.4 9:21

1377.8 9:23

2050.2 9:26

2944.6 9:30

4875.1 9:40

5101.8 9:45

Calculate the average flow rate of water into the tank between the following times:

• Between 9:17 and 9:21, average flow = GPM

Then, compare the average flow rates taken in the first three intervals with the average flow rate over the sum of those intervals (9:17 to 9:26). What does this tell us about the calculation of water flow based on volume and time measurements?

• Identify the arithmetic operations needed to compute rates of change, such as flow.

• This sort of repetitive calculation lends itself well to a programmable calculator, or to a spreadsheet program running on a personal computer. If you have some familiarity with spreadsheets, try building one to calculate average flow rate given this table of volume values!

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Question 5

A small-scale biodiesel manufacturing plant records the production of biodiesel fuel by measuring the liquid level in a storage vessel. There is no flow transmitter monitoring flow rate into the vessel, but we can infer flow rate by monitoring vessel level over time.

LT

Ultrasonic

Level transmitter

Biodiesel Storage

vessel

Computer LIU PV

The liquid level measurement signal coming from the ultrasonic level transmitter (LT) is our process variable (PV), and it is sent to a computer to be indicated and processed (LIU). The particular processing done in the computer is calculation of average flow between sample intervals.

Suppose that the computer samples the transmitter’s signal once every minute and records these measurements in a data file. Here is an example of that file’s contents after one tank-filling batch, shown in a table format:

Time Volume Time Volume Time Volume

(minutes) (gallons) (minutes) (gallons) (minutes) (gallons)

0 17.05 10 31.12 20 40.15

1 17.05 11 33.89 21 42.22

2 17.05 12 36.69 22 44.60

3 17.05 13 39.40 23 47.16

4 17.05 14 40.15 24 50.00

5 17.05 15 40.15 25 52.85

6 20.06 16 40.15 26 55.76

7 23.01 17 40.15 27 58.64

8 25.44 18 40.15 28 61.53

9 28.23 19 40.15 29 64.31

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Time

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

Volume (gallons)

5 10 15 20 25 30

(minutes)

Just looking at this graph, what can you determine about the flow rate of biodiesel into this vessel?

What would account for the “flat” spot in the middle of the graph? What do the minute variations in slope in the other areas of the graph represent, in terms of flow into the vessel?

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Now, use the data in the table to calculate and plot the flow rate of biodiesel in gallons per minute into this vessel:

Time

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

Volume (gallons)

5 10 15 20 25 30

(minutes)

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Flow (gal/min)

How do these two plots relate to each other? That is, how does the shape of one refer to the shape of the other, geometrically?

• Suppose a technician decided to calculate the flow rate at t = 4 minutes by taking the volume at that time (17.05 gallons) and dividing by the time (4 minutes). Explain why this would yield an incorrect value for flow, then explain the correct way to calculate flow rate at that time from the given data.

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